Taylor.] <jlv) [Oct. 21, 



bers (consequent upon other scales of progression) unfortunately so often 

 required to be made, the relief of a simple addition or multiplication in 

 the homogeneous units of our common scale, is too striking not to excite 

 a feeling of admiration for the easier process. It appears not to be gene- 

 rally considered, however, that this facility of computation is in no respect 

 due to the series of "tens" by which we count, but is derived exclusively 

 from the admirable notation in which the series has been clothed, and 

 through which alone, we are in modern times made acquainted with it ; 

 and from the perfect conformity of the notation to the series. Any other 

 scale will be found to exhibit an equal facility, if the same notation be 

 employed, and made to correspond strictly with the selected scale. If, 

 like the old Arabian philosophers, or like the ancient Greeks and Romans, 

 we were compelled to calculate by a set of alpJiahetic numerals, we 

 should be able to better realize how much we are indebted to that simple 

 and yet grand invention of India, the "cypher figures," or the set of 

 figures with the device of local value.* This system of numerical lan- 

 guage presents us with a formula of geometrical progressions, so illimit- 

 able in range, and j^et so perfect in its conciseness and distinctness, that it 

 transcends all conception that the ingenuity of man in all coming time 

 shall ever be able to improve it. 



Though from a remote antiquity familiar to the Hindoos (that wonder- 

 ful people from whom the civilized world has derived so much), it was 

 wholly unknown to the nations of the earth until comparatively modern 

 times ; having been first introduced into Arabia, less than a thousand 

 years ago, and from thence by slow and successive centuries into the 

 various languages of Europe. 



However much the Arabian philosopher to whom belongs the honor of 

 having first transplanted the Sanscrit Arithmetic into his own country, 

 may have been impressed with its great power and beauty, he could hardly 

 have appreciated, to its full extent, the importance and magnitude of the 

 gift he was instrumental in presenting to the civilized world ; a transfer 

 which Sir John Bowring in his "Decimal System" (chap, ii, p. 22) has 

 characterized as " the greatest step ever made towards the introduction of 

 a universal language among the nations of the world." The Hindoo 

 numerals, from the channel of their introduction into Europe, were gen- 

 erally called the "Arabic figures" — a title they still commonly retain, 

 though it is one hardly just to the people with whom these figures had 

 their origin. 



Now although this Hindoo notation has never been popularly applied 

 to any other than the decimal scale, it is obviously a formula of universal 

 applicability ; and if made use of to express a system of figures with any 

 other radix than ten, would give the same facility to all calculations per- 

 formed by that system. 



Abstracting, for a moment, all specific value from the terms "units," 

 "tens," "hundreds," and "thousands," and regarding them merely as 



* See note A, page 367. 



